All character tables of the sf CAS table library (see NPP84) are available in GAP, too. This sublibrary has been completely revised before it was included in GAP, for example, errors have been corrected and power maps have been completed.
Any sf CAS table is accessible by each of its sf CAS names, that is, the table name or the filename used in sf CAS (see CharacterTable).
gap> tbl:= CharacterTable( "m10" ); CharacterTable( "A6.2_3" )
CASInfo( tbl ) A
Let tbl be an ordinary character table tbl in the GAP library that was contained already in the sf CAS table library. When one fetches tbl from the library, one does in general not get the original sf CAS table. Namely, in many cases (mostly ATLAS tables, see ATLAS Tables) not only the identifier of the table (see Identifier) but also the ordering of classes and characters is different for the table in sf CAS and its GAP version.
Note that in several cases, the sf CAS library contains different tables of the same group, in particular these tables may have different names and orderings of classes and characters.
The CASInfo value of tbl, if stored, is a list of records,
each describing the relation between tbl and a character table in the
sf CAS library.
The records have the components
name
permchars and permclasses Irr values and the classes of tbl,
respectively, that must be applied in order to get the orderings in
the original sf CAS table, and
text
gap> HasCASInfo( tbl );
true
gap> CASInfo( tbl );
[ rec( name := "m10", permchars := (3,5)(4,8,7,6), permclasses := (),
text := "names: m10\norder: 2^4.3^2.5 = 720\nnumber of classes: \
8\nsource: cambridge atlas\ncomments: point stabilizer of mathieu-group m1\
1\ntest: orth, min, sym[3]\n" ) ]
The class fusions stored on tables from the sf CAS library have been
computed anew;
the text component of such a fusion record tells if the fusion map is equal
to that in the sf CAS library
--of course modulo the permutation of classes between the table in sf CAS
and its GAP version.
gap> First( ComputedClassFusions( tbl ), x -> x.name = "M11" ); rec( name := "M11", map := [ 1, 2, 3, 4, 5, 4, 7, 8 ], text := "fusion is unique up to table automorphisms,\nthe representative is \ equal to the fusion map on the CAS table" )
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GAP 4 manual